Iteration of the number-theoretic function \(f(2n)=n\), \(f(2n+1)=3n+2\)

DOI10.1016/0001-8708(77)90087-1zbMath0352.10001OpenAlexW2013547425MaRDI QIDQ1235725

C. J. Everett

Publication date: 1977

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(77)90087-1

Mathematics Subject Classification ID

Recurrences (11B37) Special sequences and polynomials (11B83)

Related Items (20)

T. Tao and the Syracuse conjecture ⋮ On the arithmetic of cycles for the Collatz-Hasse (`Syracuse') conjectures ⋮ A generalization of Everett's result on the Collatz \(3x+1\) problem ⋮ Iterates of Number Theoretic Functions with Periodic Rational Coefficients (Generalization of the 3x+ 1 Problem) ⋮ Statistical properties of an iterated arithmetic mapping ⋮ Collatz Meets Fibonacci ⋮ A remark about the density of the orbits of the Collatz permutation ⋮ Is the Syracuse falling time bounded by 12? ⋮ Analogues of the 3x+ 1 Problem in Polynomial Rings of Characteristic 2 ⋮ The \(3x+1\) problem: a lower bound hypothesis ⋮ A geometric approach to divergent points of higher dimensional Collatz mappings ⋮ Koopman Operators and the $3x+1$-Dynamical System ⋮ On a generalization of the \(3x+1\) problem ⋮ On the \(3x+1\) problem ⋮ On the almost sure convergence of Syracuse sequences ⋮ Unnamed Item ⋮ Eine Bemerkung zum Hasse-Syracuse-Algorithmus ⋮ Parity sequences of the 3x+1 map on the 2-adic integers and Euclidean embedding ⋮ Circular slider graphs: de Bruijn, Kautz, Rauzy, lamplighters and spiders ⋮ Almost all orbits of the Collatz map attain almost bounded values

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